The mass of a proton is $1.0073 \, u$ and that of a neutron is $1.0087 \, u$. The binding energy of $_2He^4$ is .... ($u = \text{atomic mass unit}$,mass of helium nucleus = $4.0015 \, u$)

$A$ free nucleus of mass $24 \, amu$ emits a gamma photon (when initially at rest). The energy of the photon is $7 \, MeV$. The recoil energy of the nucleus in $keV$ is:

Consider the nuclear reaction $X^{200} \rightarrow A^{110} + B^{90}$. If the binding energy per nucleon for $X, A,$ and $B$ is $7.4 \, MeV, 8.2 \, MeV,$ and $8.2 \, MeV$ respectively, what is the energy released in $MeV$?

Assertion : The binding energy per nucleon,for nuclei with atomic mass number $A > 100$,decreases with $A$.
Reason : The nuclear forces are weak for heavier nuclei.

The graph shows the binding energy per nucleon versus mass number. $A, B, C, D, E, F$ are different nuclei. Four processes are given where $\varepsilon$ is the energy released. In which process is $\varepsilon > 0$?
$(i) \, A + B \rightarrow C + \varepsilon$
$(ii) \, C \rightarrow A + B + \varepsilon$
$(iii) \, D + E \rightarrow F + \varepsilon$
$(iv) \, F \rightarrow D + E + \varepsilon$

$A$ plot of the number of neutrons $(N)$ against the number of protons $(Z)$ for stable nuclei exhibits upward deviation from linearity for atomic number $Z > 20$. For an unstable nucleus having an $N/Z$ ratio less than $1$,the possible mode$(s)$ of decay is(are):
$(A)$ $\beta^{-}$-decay ($\beta$ emission)
$(B)$ Orbital or $K$-electron capture
$(C)$ Neutron emission
$(D)$ $\beta^{+}$-decay (positron emission)